The problem with Kasich is that, like almost everyone else, he’s a liar.
Whether or not we win an election by electing a liar simply doesn’t matter, because by electing a liar, we lose.
V.P.’s just not that important in the grand scheme of things. If I like the guy at the top, I don’t really care who he picks as V.P. It won’t change my vote.
If the difference between winning or losing the election means signing on Kasich to shore up Ohio, then it’s worth it to do it. Securing Ohio early leaves Trump more time to work on Virginia, Florida, Pennsylvania, etc.
Kasich would not need to have any influence on foreign policy or social issues as V.P., but as someone who could help craft a balanced budget proposal for Trump, he could prove useful.
Also, as a more seasoned politician, Kasich would be less likely to make gaffes like Carson would. When you have someone like Trump at the top, it’s better to have someone bland as V.P. who won’t make waves. Trump will have enough trouble sticking to his own message without having to clean up what his V.P. says.